The D-backs, Orioles and Pirates are three of the teams showing the most interest in Norris, a source told MLB.com, but no deal is imminent.
"They scratched me for a lot of reasons," he said. "So it's a little unfortunate. I wanted to go out there and pitch, but I understand there's a lot of stuff flying around me. I'm here to support my teammates tonight and just go out and see what happens.
"I just have to be prepared for both ends of it. You could stay, you could go. So I've been concentrating on pitching here, and that's what I've done for the last four years, and it hasn't changed yet, so that's the way my focus is going to be. It's out of my hands."
Porter told reporters prior to Tuesday's game that trade talks with Norris were intensifying.
"It's one of those things, from an organization standpoint, you have a guy that has attracted a lot of interest from other ballclubs," Porter said. "You look at the Trade Deadline looming and it just made more sense to not risk injury at this juncture of the conversation, because the conversations have gotten a little deeper and Bud has been made well aware of why we decided to scratch him today with the notion there is a possibility he might get traded.
"There is also a possibility he remains with us. But with today being the day before the Trade Deadline, we decided to lean on the side of not risking anything."
Even as he repeatedly checked his phone in the clubhouse for updates from his agent, Norris found time to escape the rumor mill by playing cards with teammates -- the same teammates who stood behind him and jokingly read a fake report from the television that he had been traded.
Norris wouldn't handicap whether he would be with the Astros in a day.
"I don't know," he said. "I don't want to put any numbers on it. Everybody speculates where I could go and stuff like that. It's out of my hands. It's the GM and the front office, and I just want to play baseball for wherever I am. And right now, I'm still an Astro, and that's where my focus is."
Norris, 28, is 6-9 with a 3.93 ERA in 21 starts and is on pace to throw 200 innings for the first time in his career. Norris is making $3 million this year in his first year of arbitration and would certainly be attractive to a team, considering he's under club control for two more seasons.
Norris is 0-2 with an 8.47 ERA in his last three starts after going 2-3 with a 2.29 ERA in his eight starts prior to those three.
Norris, the longest-current-tenured member of the team, has seen more than 12 trades in the last few years, with many teammates leaving Houston for greener pastures. He admits he can't help but wonder what it would be like to pitch for a contender.
"Absolutely," he said. "That's why you play the game, is to compete and go out and win. We've been through it the last couple of years here, but to see 10-plus players I've seen [traded] in my four years is pretty crazy, and I know now that maybe I'm the next piece ...
"Like I said, I just want what's best for me and my family and my future, and I'm very thankful for the Astros and everything they gave me. If they decide otherwise, I understand the reasons behind it and I still wish them well. I have to be a little selfish and take care of myself."
Norris admitted the last few days have been nerve-wracking.
"And exciting at the same time," he said. "My emotions are here and there and everywhere. I'm glad I had an off-day [Monday] to give me time to relax and rest up. The next 24 hours will be pretty interesting."
On Monday, the Astros dealt closer Jose Veras to the Tigers for outfield prospect Danry Vasquez and a player to be named, which was just the latest in a series of deals made by Astros general manager Jeff Luhnow in which he flipped a veteran player for prospects.
Harrell, who was the Astros' best pitcher last year, was pulled from the rotation on July 5 after nine starts. He was 5-9 with a 5.04 ERA as a starter and is 0-1 with a 6.35 ERA in four games as a reliever. He last pitched Thursday in Toronto, throwing three innings and allowing three runs.